Nonadiabatic Transitions : Concepts, Basic Theories and Applications

by Nakamura, Hiroki

• ISBN13: 9789810247195
• ISBN10: 9810247192
• Format: Hardcover
• Copyright: 2002-08-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

Nonadiabatic transition is a highly multidisciplinary concept and phenomenon, constituting a fundamental mechanism of state and phase changes in various dynamical processes of physics, chemistry and biology, such as molecular dynamics, energy relaxation, chemical reaction, and electron and proton transfer.

Table of Contents

Preface	v
Introduction: What is ``Nonadiabatic Transition''?	1	(6)
Multi-Disciplinarity	7	(12)
Physics	7	(6)
Chemistry	13	(3)
Biology	16	(1)
Economics	16	(3)
Historical Survey of Theoretical Studies	19	(22)
Landau-Zener-Stueckelberg Theory	19	(9)
Rosen-Zener-Demkov Theory	28	(3)
Nikitin's Exponential Model	31	(2)
Nonadiabatic Transition Due to Coriolis Coupling and Dynamical State Representation	33	(8)
Background Mathematics	41	(12)
Wentzel-Kramers-Brillouin Semiclassical Theory	41	(4)
Stokes Phenomenon	45	(8)
Basic Two-State Theory for Time-Independent Processes	53	(68)
Exact Solutions of the Linear Curve Crossing Problems	53	(12)
Landau-Zener type	53	(9)
Nonadiabatic tunneling type	62	(3)
Complete Semiclassical Solutions of General Curve Crossing Problems	65	(24)
Landau-Zener (LZ) type	66	(5)
E ≥ Ex (b2 ≥ 0)	71	(2)
E ≤ Ex (b2 ≤ 0)	73	(1)
Numerical examples	74	(4)
Nonadiabatic Tunneling (NT) Type	78	(3)
E ≤ Et (b2 ≤ -1)	81	(1)
Et ≤ E ≤ Eb (|b2| ≤ 1)	82	(1)
E ≥ Eb (b2 ≥ 1)	83	(1)
Complete reflection	84	(1)
Numerical examples	85	(4)
Non-Curve-Crossing Case	89	(4)
Rosen-Zener-Demkov model	89	(1)
Diabatically avoided crossing model	90	(3)
Exponential Potential Model	93	(15)
Mathematical Implications	108	(13)
Case (i)	112	(3)
Case (ii)	115	(3)
Case (iii)	118	(3)
Basic Two-State Theory for Time-Dependent Processes	121	(24)
Exact Solution of Quadratic Potential Problem	121	(5)
Semiclassical Solution in General Case	126	(9)
Two-crossing case: β ≥ 0 (see Fig. 6.1 (a))	126	(3)
Diabatically avoided crossing case: β ≤ 0 (see Fig. 6.1(b))	129	(6)
Other Exactly Solvable Models	135	(10)
Two-State Problems	145	(16)
Diagrammatic Technique	145	(5)
Inelastic Scattering	150	(1)
Elastic Scattering with Resonances and Predissociation	151	(4)
Perturbed Bound States	155	(3)
Time-Dependent Periodic Crossing Problems	158	(3)
Effects of Dissipation and Fluctuation	161	(8)
Multi-Channel Problems	169	(30)
Exactly Solvable Models	169	(7)
Time-independent case	169	(2)
Time-dependent case	171	(5)
Semiclassical Theory of Time-Independent Multi-Channel Problems	176	(18)
General framework	179	(1)
Case of no closed channel (m = 0)	180	(1)
Case of m ≠ 0 at energies higher than the bottom of the highest adiabatic potential	180	(2)
Case of m ≠ 0 at energies lower than the bottom of the highest adiabatic potential	182	(3)
Numerical example	185	(9)
Time-Dependent Problems	194	(5)
Multi-Dimensional Problems	199	(34)
Classification of Surface Crossing	200	(3)
Crossing seam	200	(1)
Conical intersection	201	(1)
Renner-Teller effect	202	(1)
Reduction to One-Dimensional Multi-Channel Problem	203	(25)
Linear Jahn-Teller problem	203	(7)
Collinear chemical reaction	210	(5)
Three-dimensional chemical reaction	215	(13)
Semiclassical Propagation Method	228	(5)
Complete Reflection and Bound States in the Continuum	233	(24)
One NT-Type Crossing Case	233	(7)
Diabatically Avoided Crossing (DAC) Case	240	(8)
Two NT-Type Crossings Case	248	(9)
At energies above the top of the barrier: (Eu, ∞)	248	(1)
At energies between the barrier top and the higher crossing: (E+, Eu)	249	(2)
At energies in between the two crossing regions: (E-, E+)	251	(1)
At energies below the crossing points: (-∞, E-)	252	(1)
Numerical examples	252	(5)
New Mechanism of Molecular Switching	257	(42)
Basic Idea	257	(1)
One-Dimensional Model	258	(23)
Transmission in a pure system	258	(9)
Transmission in a system with impurities	267	(10)
Molecular switching	277	(4)
Two-dimensional model	281	(9)
Two-dimensional constriction model	282	(3)
Wave functions, matching, and transmission coefficient	285	(5)
Numerical Examples	290	(9)
Control of Nonadiabatic Processes by an External Field	299	(44)
Control of Nonadiabatic Transitions by Periodically Sweeping External Field	300	(4)
Basic Theory	304	(10)
Usage of the Landau-Zener-Stueckelberg type transition	310	(2)
Usage of the Rosen-Zener-Demkov type transition	312	(1)
General case	313	(1)
Numerical Examples	314	(15)
Spin tunneling by a magnetic field	314	(2)
Vibrational and tunneling transitions by laser	316	(3)
Landau-Zener-Stueckelberg type transition	319	(4)
Rosen-Zener-Demkov type transition	323	(1)
General case	324	(5)
Laser Control of Photodissociation with Use of the Complete Reflection Phenomenon	329	(14)
Conclusions: Future Perspectives	343	(4)
Appendix A Final Recommended Formulas for General Time-Independent Two-Channel Problem	347	(12)
A.1. Landau-Zener Type	347	(5)
A.1.1. E ≥ Ex (crossing energy) (b2 ≥ 0)	349	(1)
A.1.2. E ≤ Ex (b2 ≤ 0)	350	(1)
A.1.3. Total scattering matrix	351	(1)
A.2. Nonadiabatic Tunneling Type (see Fig. A.2)	352	(7)
A.2.1 E ≥ Eb	355	(1)
A.2.2. Eb ≥ E ≥ Et	355	(2)
A.2.3. E ≤ Et	357	(2)
Appendix B Time-Dependent Version of the Zhu-Nakamura Theory	359	(2)
Bibliography	361	(10)
Index	371